derivative
Consider the graph y = f(x). If (x, y) are the coordinates of a general point P on the graph, and (x + Δx, y + Δy) are those of a nearby point Q on the graph, the quotient Δy/Δx is the gradient of the chord PQ. Also, Δy = f(x + Δx)−f(x). So the derivative of f at x is the limit of the quotient Δy/Δx as Δx → 0. This limit can be denoted by dy/dx, which is thus an alternative notation for f ′(x). The notation y′ is also used.
PQ's gradient approximating the curve's
The derivative f ′(a) gives the gradient of the curve y = f(x), and hence the gradient of the tangent to the curve, at (a,f(a)). If x is a function of t, where t denotes time, then the derivative dx/dt is referred to as a rate of change and may be denoted by 
. The modulus function f(x) = |x| is an example of a function which does not have a well-defined derivative at x = 0 (see also blancmange function). For the derivatives of certain common functions, see appendix 7. See also differentiation, higher derivative, left and right derivative, partial derivative.
- simple interest
- simple pendulum
- simple pole
- simple root
- simplest form
- simplex
- simplex method
- simplex tableau
- simplicial complex
- simplify
- simply connected
- Simpson's paradox
- Simpson's rule
- Simson line
- simulation
- simultaneity
- simultaneous linear differential equations
- simultaneous linear equations
- sine
- sine rule
- singleton
- Singmaster's conjecture
- singular
- singularity
- singular point